In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space.
Seven-dimensional spaces have a number of special properties, many of them related to the octonions.
This is related to Hurwitz's theorem, which prohibits the existence of algebraic structures like the quaternions and octonions in dimensions other than 2, 4, and 8.
The 6-sphere or hypersphere in seven-dimensional Euclidean space is the six-dimensional surface equidistant from a point, e.g. the origin.
In 1956, John Milnor constructed an exotic sphere in 7 dimensions and showed that there are at least 7 differentiable structures on the 7-sphere.